The theory of illumination subspaces is well developed and has been tested extensively on the Yale Face Database B (YDB) and CMU-PIE (PIE) data sets. This paper shows that if face recognition under varying illumination is cast as a problem of matching sets of images to sets of images, then the minimal principal angle between subspaces is sufficient to perfectly separate matching pairs of image sets from nonmatching pairs of image sets sampled from YDB and PIE. This is true even for subspaces estimated from as few as six images and when one of the subspaces is estimated from as few as three images if the second subspace is estimated from a larger set (10 or more). This suggests that variation under illumination may be thought of as useful discriminating information rather than unwanted noise.